Question

Determine the point(s) (if any) at which the graph of the function has a horizontal tangent line. (If the function has no horizontal tangent line, enter NONE.)

Answer 1

(0, 9)

Explanation:

We have the following function:

`y=x^2+9`

We differentiate with respect to x to calculate the differential of y, like this:

`\begin{gathered} (dy)/(dx)=(d)/(dx)(x^2+9) \\ (dy)/(dx)=2x \end{gathered}`

To find out if there is a horizontal line dy/dx is 0, and we solve for x, just like this:

`\begin{gathered} 0=2x \\ x=0 \end{gathered}`

We substitute in the function and get:

`\begin{gathered} y=0^2+9 \\ y=9 \end{gathered}`

Therefore, it has a horizontal tangent line at the point (0, 9)